# 181-Exam1 - Test 1 (Math 181) February 15, 2007 Name:_ I....

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I. questions. -6 -4 -2 0 2 4 6 2 4 -2 ) ( lim ) ( ) ( 4 4 4 x f x f x f x x x  ) 0 ( ) ( ) ( f x f x f x x Is ) ( x f y continuous at x = 0? Is ) ( x f y continuous at 0< x <4? Is ) ( x f y continuous if x =4? Is ) ( x f y differentiable at x =4? II. (5 pts) Determine whether each of the followings is true or false. 1. If 3 ) ( lim 2 x f x , 3 ) ( lim 2 x f x ,. ____________ 2. If ) 2 ( f does not exist, ) ( lim 2 x f x is undefined. ____________ 3. If 0 ) ( lim 2 x f x , 0 ) ( lim 2 x f x . ____________ 4. ) ( x f y is continuous at 2 x , if ) ( lim 2 x f x exists. ____________ 5. If ) ( x f y is differentiable at 2 x , ) ( x f y is continuous at 2 x .___________

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III . (4 pts) Find the graph of the derivative of the given function ). ( x f y ) ( x f y ) ( ' x f y IV . (3pts each) Find the limit value for each of the followings. 1. ) 4 3 ( lim 2 2 3 2 e x x x 2. h h h h 2 lim 2 0 3. 3 27 3 3 x x x 4. 7 6 7 15 70 100 35 5 x x x x x
V. (3pts each)Differentiate each of the following functions.

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## 181-Exam1 - Test 1 (Math 181) February 15, 2007 Name:_ I....

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